We remark that Keating and Rudnick have a more precise expression in [1]}. Indeed, by (REF ),
\(\sum _{\begin{array}{c}f\in \mathcal {M}_n\\f(0)\ne  0\end{array}}\Lambda _k(f) =(q-1)^k\sum _{m=0}^\infty \binom{-k}{m} \binom{-k}{n-k-m} (-1)^{n-k} q^{n-k-m}.\) 
